Question

1／2×4＋1／6×8＋...＋1／2006×2008＋1／4×6＋1／8×10＋...＋1／2004×2006数学简便方法计算

Answer 1

1/2（1/2-1/4+1/6-1/8+……+1/2006-1/2008）+1/2（1/4-1/6+1/8-1/10……+1/2004-1/2006）=1003/4016
分母之间相差多少就乘以几分之一

Answer 2

解：1／2×4＋1／6×8＋...＋1／2006×2008＋1／4×6＋1／8×10＋...＋1／2004×2006
=1／2×4＋1／4×6＋1／6×8＋1／8×10＋...＋1／2004×2006＋1／2006×2008
=1/2[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+……+ (1/2006-1/2008)]
=1/2(1/2-1/2008)
=1/2(1004/2008-1/2008)
=1/2*1003/2008
=1003/4016

Answer 3

1/2*4+1/6*8+......1/2006*2008+1/4*6+1/8*10......+1/2004*2006
=1/2*4+1/4*6+1/6*8+1/8*10+......1/2004*2006+1/2006*2008
=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+...+1/2004-1/2006+1/2006+1/2008)÷2
=(1/2-1/2008)/2
=1003/5016

Answer 4

1/2×（1/2-1/4+1/4-1/6+1/6-1/8+…+1/2006-1/2008）=1/2×（1/2-1/2008）=2013/5016

Answer 5

1/4×（1-1/2+1/2-1/3+1/3-1/4+…+1/1003-1/1004）=1/4×（1-1/1004）=1003/4016